This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Define the resistance of each wire. The resistance R of a wire is given by the formula R = (L)/(A), where is the resistivity, L is the length, and A is the cross-sectional area. Given that the two wires have the same size, let their length be L and their cross-sectional area be A. For the first wire with resistivity _1: R_1 = _1 (L)/(A) For the second wire with resistivity _2: R_2 = _2 (L)/(A) Step 2: Calculate the equivalent resistance of the series combination. When two resistors are connected in series, their equivalent resistance R_eq is the sum of their individual resistances: R_eq = R_1 + R_2 Substitute the expressions for R_1 and R_2: R_eq = _1 (L)/(A) + _2 (L)/(A) R_eq = (_1 + _2) (L)/(A) Step 3: Express the equivalent resistance in terms of equivalent resistivity. When the two wires are connected in series, they form a single composite wire. The total length of this composite wire is L_total = L + L = 2L. The cross-sectional area of the composite wire remains A. Let the equivalent resistivity of this combination be _eq. Then, the equivalent resistance can also be written as: R_eq = _eq L_totalA R_eq = _eq (2L)/(A) Step 4: Equate the two expressions for R_eq and solve for _eq. From Step 2 and Step 3, we have: (_1 + _2) (L)/(A) = _eq (2L)/(A) We can cancel out the common term (L)/(A) from both sides: _1 + _2 = 2 _eq Now, solve for _eq: _eq = (_1 + _2)/(2) The equivalent resistivity of the combination is (_1 + _2)/(2). Comparing this result with the given options: [A] sqrt(_1_2) [B] 2(_1 + _2) [C] (_1 + _2)/(2) [D] _1 + _2 The calculated equivalent resistivity matches option [C]. The final answer is C. Last free one today — make it count tomorrow, or type /upgrade for unlimited.